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The wooden beam (E = 10 GPa) is loaded as shown. Using the Method of Superposition, find the slope at A and the vertical deflection at C. 4 kN 4 kN A C -1.5 m 1.5 m- + 3 m |В 100 m 200 m

The wooden beam (E = 10 GPa) is loaded as shown. Using the Method of Superposition, find the slope at A and the vertical deflection at C. 4 kN 4 kN A C -1.5 m 1.5 m- + 3 m |В 100 m 200 m

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The wooden beam (E = 10 GPa) is loaded as shown. Using the Method of Superposition, find the slope at A and the vertical deflection at C. 4 kN 4 kN A C ◄1.5 m▬▬▬▬1.5 m- -3 m B 100 m 1200 m
Transcribed Image Text:The wooden beam (E = 10 GPa) is loaded as shown. Using the Method of Superposition, find the slope at A and the vertical deflection at C. 4 kN 4 kN A C ◄1.5 m▬▬▬▬1.5 m- -3 m B 100 m 1200 m
APPENDIX D EQUATIONS FOR DEFLECTIONS OF SIMPLY SUPPORTED BEAMS SIMPLY SUPPORTED BEAMS LENGTH, L y₁ A. A A dy dx dy dx M dy dx dy dx Max L/2 Max dy dx a L/2 dy dx F y Max do 9 dy dx R -У мах dx dy dx L/2 dx/B B B B B X B 90 dy dx dx dy dx dx dy dx dy dx dy dx SLOPE Max B dy dx B Max B A -FL² 16EI -Fab(L+ b) 6EI L Fab(L+ a) 6EI L ML 3EI ML 6EI, = 9,L³ 24EI, 3q,L³ 128EI, 79, L³ 384EI, dy -79,L³ dx 360EI 9,L³ dx B 45EI, y y = У мах y x=a У мах y: y = -Fbx y = (L²-b²-x²) 6EI L 0≤x≤a y = y = = DEFLECTION EQUATIONS -Fx 48EI, У мах -Mx 6EIL Умау = -FL³ 48EL, -Fba 6EI,L -(3L² - 4x²) -90x 24EI, -qox 384EI, = -ML² 243EI 0≤x≤L/2 -(x² -3Lx+2L²) (L²-b²-a²) -59, L¹ У мах 384EI, -90L 384EI, +17L²x-L³) L/2≤x≤L -90x 360EI L zat x = 0.4226L (x³ - 2Lx² + L³) -(16x³-24Lx² +9L³) 0≤x≤L/2 -(8x³-24Lx² -6.563×10qL* EL z at x = 0.4598L -(3x4 -10L²x² +7L¹) -6.52 × 10-³q,L¹ EI, at x = 0.5193
Transcribed Image Text:APPENDIX D EQUATIONS FOR DEFLECTIONS OF SIMPLY SUPPORTED BEAMS SIMPLY SUPPORTED BEAMS LENGTH, L y₁ A. A A dy dx dy dx M dy dx dy dx Max L/2 Max dy dx a L/2 dy dx F y Max do 9 dy dx R -У мах dx dy dx L/2 dx/B B B B B X B 90 dy dx dx dy dx dx dy dx dy dx dy dx SLOPE Max B dy dx B Max B A -FL² 16EI -Fab(L+ b) 6EI L Fab(L+ a) 6EI L ML 3EI ML 6EI, = 9,L³ 24EI, 3q,L³ 128EI, 79, L³ 384EI, dy -79,L³ dx 360EI 9,L³ dx B 45EI, y y = У мах y x=a У мах y: y = -Fbx y = (L²-b²-x²) 6EI L 0≤x≤a y = y = = DEFLECTION EQUATIONS -Fx 48EI, У мах -Mx 6EIL Умау = -FL³ 48EL, -Fba 6EI,L -(3L² - 4x²) -90x 24EI, -qox 384EI, = -ML² 243EI 0≤x≤L/2 -(x² -3Lx+2L²) (L²-b²-a²) -59, L¹ У мах 384EI, -90L 384EI, +17L²x-L³) L/2≤x≤L -90x 360EI L zat x = 0.4226L (x³ - 2Lx² + L³) -(16x³-24Lx² +9L³) 0≤x≤L/2 -(8x³-24Lx² -6.563×10qL* EL z at x = 0.4598L -(3x4 -10L²x² +7L¹) -6.52 × 10-³q,L¹ EI, at x = 0.5193
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